$$ \begin{aligned} (\frac{2}{3}-1)(\frac{1}{2}x+3) &= 0&& \text{simplify left side} \\[1 em](-\frac{1}{3})(\frac{x}{2}+3) &= 0&& \\[1 em](-\frac{1}{3})\frac{x+6}{2} &= 0&& \\[1 em]\frac{-x-6}{6} &= 0&& \text{multiply ALL terms by } \color{blue}{ 6 }. \\[1 em]6 \cdot \frac{-x-6}{6} &= 6\cdot0&& \text{cancel out the denominators} \\[1 em]-x-6 &= 0&& \text{ move the constants to the right } \\[1 em]-x &= 6&& \text{switch signs on both sides} \\[1 em]x &= -6&& \\[1 em] \end{aligned} $$

This page was created using